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Simplifying 4x2 + -41 = 12x Reorder the terms: -41 + 4x2 = 12x Solving -41 + 4x2 = 12x Solving for variable 'x'. Reorder the terms: -41 + -12x + 4x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -41 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.25 + -3x + x2 = 0 Move the constant term to the right: Add '10.25' to each side of the equation. -10.25 + -3x + 10.25 + x2 = 0 + 10.25 Reorder the terms: -10.25 + 10.25 + -3x + x2 = 0 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + -3x + x2 = 0 + 10.25 -3x + x2 = 0 + 10.25 Combine like terms: 0 + 10.25 = 10.25 -3x + x2 = 10.25 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 10.25 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 10.25 + 2.25 Combine like terms: 10.25 + 2.25 = 12.5 2.25 + -3x + x2 = 12.5 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + -1.5) equal to 3.535533906 and -3.535533906.Subproblem 1
x + -1.5 = 3.535533906 Simplifying x + -1.5 = 3.535533906 Reorder the terms: -1.5 + x = 3.535533906 Solving -1.5 + x = 3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.535533906 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.535533906 + 1.5 x = 3.535533906 + 1.5 Combine like terms: 3.535533906 + 1.5 = 5.035533906 x = 5.035533906 Simplifying x = 5.035533906Subproblem 2
x + -1.5 = -3.535533906 Simplifying x + -1.5 = -3.535533906 Reorder the terms: -1.5 + x = -3.535533906 Solving -1.5 + x = -3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.535533906 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.535533906 + 1.5 x = -3.535533906 + 1.5 Combine like terms: -3.535533906 + 1.5 = -2.035533906 x = -2.035533906 Simplifying x = -2.035533906Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.035533906, -2.035533906}
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